JEE Main 2023 — Circle Question with Solution

Let a circle $$C_1$$ be obtained on rolling the circle $$x^2+y^2-4x-6y+11=0$$ upwards 4 units on the tangent $$\mathrm{T}$$ to it at the point $$(3,2)$$. Let $$C_2$$ be the image of $$C_1$$ in $$\mathrm{T}$$. Let $$A$$ and $$B$$ be the centers of circles $$C_1$$ and $$C_2$$ respectively, and $$M$$ and $$N$$ be respectively the feet of perpendiculars drawn from $$A$$ and $$B$$ on the $$x$$-axis. Then the area of the trapezium AMNB is :